653

653 is a prime number. It is a Sophie Germain prime because 2 x 653 + 1 = 1307 is a prime.

653 is the first three-digit prime number to occur in the decimal expansion of pi.

653 has a representation as a sum of two squares: 653 = 13² + 22².

653 is the hypotenuse of a primitive Pythagorean triple: 653² = 315² + 572².

653 is the sum of the squares of five consecutive primes: 653 = 5² + 7² + 11² + 13² + 17².

ARINC 653 is a software specification for space and time partitioning in safety-critical avionics real-time operating systems.

Source: Number Gossip

659

659 is a prime number. It is a Sophie Germain prime because 2 x 659 + 1 = 1319 is also a prime.

0659, 2659, 3659, 5659, and 6659 are all primes.

659 and 661 form a twin prime pair.

659 is a divisor of 12⁷ - 1.

659 is the sum of seven consecutive primes: 659 = 79 + 83 + 89 + 97 + 101 + 103 + 107.

659 Nestor is a Jupiter Trojan asteroid that orbits along Jupiter's path. It was discovered in 1908.

Source: Prime Curios!

179

179 is a prime number. 179 is a Sophie Germain prime because 2 x 179 + 1 = 359, a prime.

179 and 181 form a twin prime pair.

179 = (17 x 9) + (17 + 9).

179 has a square comprised of the digits 0 to 4: 179² = 32041.

179 x 79 = 14141.

There are 179 even days in one year.

Source: Number Gossip

419

419 is a prime number.

419 is also a Sophie Germain prime because 2 x 419 + 1 = 839 is also prime. It is the 22nd Sophie Germain prime, and 22 = 2 x 11 is the product of two Sophie Germain primes.

419 and 421 form a twin prime pair.

419 is a divisor of 13¹¹ - 1.

419 is the smallest number that when divided by 2, 3, 4, 5, 6, and 7 leaves remainders of 1, 2, 3, 4, 5, and 6, respectively. Also, 419 is 1 less than the least common multiple of the first seven integers.

419, 41, and 19 are all primes. Their reversals, 914, 14, and 91, are all semiprimes.

Dutch naturalist and microscopy pioneer Anton van Leeuwenhoek (1632-1723) ground a total of 419 lenses during his life.

Source: Prime Curios!

359

359 is a prime number. It is a Sophie Germain prime because 2 x 359 + 1 = 719, a prime.

359 is a number that cannot be written as a sum of three squares.

359 = -1 + 2³ x 45.

The 359th, 360th, and 361st decimal digits of pi are 360.

359 has a base 3 representation (111022) that ends with its base 7 representation (1022), which is also true for 357 and 358.

In the Star Trek imaginary universe, the Battle of Wolf 359 was the Federation's first major battle against a group of cyborgs.

Source: Prime Curios!

173

173 is a prime number. It is a Sophie Germain prime because 2 x 173 + 1 = 347, which is also prime.

173 has a representation as a sum of two squares: 173 = 2² + 13². It is the sum of the squares of two Fibonacci numbers, 2 and 13.

173 is the hypotenuse of a primitive Pythagorean triple: 173² = 52² + 165².

173 is the only prime whose sum of cubed digits equals its reversal: 1³ + 7³ + 3³ = 371.

173 is the largest known prime whose square (29929) and cube (5177717) have no digits in common.

173 = 1 + 2² + 2³ + 2⁵ + 2⁷, where the exponents are consecutive primes.

In the 1993 movie The Sandlot, The Beast (a ferocious dog) is said to have eaten 173 guys.

Source: Prime Curios!

683

683 is a prime number. It is a Sophie Germain prime because 2 x 683 + 1 is also a prime number.

683 is also a Wagstaff prime because it has the form (2^q + 1)/3, where q is another prime, 11.

683 is a divisor of 4¹¹ - 1.

683 is 838 in base 9.

The submarine USS Parche (SSN-683) was named for a small, coral-reef butterflyfish.

Source: What's Special About This Number?

809

809 is a prime number. It is a Sophie Germain prime because 2 x 809 + 1 = 1619 is also a prime.

809 has a representation as a sum of two squares: 809 = 5² + 28².

809 and 811 form a twin prime pair.

809 is the hypotenuse of a primitive Pythagorean triple: 809² = 280² + 759².

809 is a divisor of 44⁸ - 1.

809 is the only three-digit pime. Pimes are primes whose digits contain circles (that is, use only 0, 6, 8, and 9).

809 was the hotel room number in the 1952 film Don't Bother to Knock, starring Richard Widmark and Marilyn Monroe.

Source: Number Gossip

3

3 is a prime number. 3 is also a Sophie Germain prime because 2 x 3 + 1 = 7, which is a prime.

3 is the second triangular number, or the sum of the first two positive integers: 3 = 1 + 2.

3 is the fourth Fibonacci number: 1, 1, 2, 3, 5, 8, 13, 21, . . .

3 is the second Lucas number: 1, 3, 4, 7, 11, 18, 29, . . .

3 has a unique representation as a sum of three squares: 3 = 1² + 1² + 1².

3 is the number of integer partitions of 3.

3 is the number of integer partitions of 5 into distinct parts.

3 and 5 form a twin prime pair.

Tri- means three. So triangles have three sides, a tripod has three legs, and the dinosaur triceratops had three horns. The French flag is a tricolore because it has three colors.

Three-dimensional means that something has length, width, and depth.

The letters A F H K N Y Z are all made up of three lines.

The trillium, Ontario's provincial flower, has three petals.

Source: R. Phillips. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

9293

9293 is a prime number. It is also a Sophie Germain prime because 2 x 9293 + 1 = 18587, which is also a prime.

9293 reversed is also a prime: 3929. 9293 is the largest number formed from two consecutive two-digit numbers that is also a prime when reversed.

9293 has a representation as a sum of two squares: 9293 = 58² + 77².

9293 is the hypotenuse of a primitive Pythagorean triple: 9293² = 2565² + 8932².

9293 Kamogata is a main-belt asteroid discovered in 1982.

Source: Prime Curios!

593

593 is a prime number. It is a Sophie Germain prime because 2 x 593 + 1 = 1187 is also prime.

593 has a representation as a sum of two squares: 593 = 8² + 23².

593 is the hypotenuse of a primitive Pythagorean triple: 593² = 368² + 465².

593 = 9² + 2⁹ = 3^2*2 + 2^3*3.

593 is the number on the conning tower of the submarine USS Wayne in the movie The Spy Who Loved Me.

Source: Prime Curios!

53

53 is a prime number. It is also a Sophie Germain prime because 2 x 53 + 1 = 107, which is also a prime.

5 and 3 are the eighth and ninth decimal digits of pi.

53 has a representation as a sum of two squares: 53 = 2² + 7².

53 is the hypotenuse of a primitive Pythagorean triple: 53² = 28² + 45².

53 is the sum of five consecutive primes: 5 + 7 + 11 + 13 + 17 = 53.

The chemical element iodine has atomic number 53.

Source: Prime Curios!

293

293 is a prime number.

293 is a Sophie Germain prime because 2 x 293 + 1 = 587, which is also a prime.

293 has a representation as a sum of two squares: 293= 2² + 17².

293 is the hypotenuse of a primitive Pythagorean triple: 293² = 68² + 285².

293 Brasilia is a large asteroid discovered in 1893.

Source: Prime Curios!

281

281 is a prime number. It is also a Sophie Germain prime because 2 x 281 + 1 = 563 is prime.

281 has a representation as a sum of two squares: 281 = 5² + 16².

281 and 283 form a twin prime pair.

281 is the hypotenuse of a primitive Pythagorean triple: 281² = 160² + 231².

The final repeated digit-products of consecutive integers 281, 282, and 283 are all 6: 2 x 8 x 1 = 16, 1 x 6 = 6; 2 x 8 x 2 = 32, 3 x 2 = 6; 2 x 8 x 3 = 48, 4 x 8 = 32, 3 x 2 = 6. There are no four consecutive integers with the same final digit-product less than 6 x 24 x 10⁸.

281 is the sum of the first 14 primes (up to 43). If we add consecutive primes up to 281, the total is also a prime (7699). There are no other such primes with this behavior between 281 and 7699.

281 is a telephone area code for Houston, Texas.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

131

131 is a prime number. It is a Sophie Germain prime because 2 x 131 + 1 = 263 is also prime.

The 131st Fibonacci number (1066340417491710595814572169) is the smallest Fibonacci prime that contains all the digits from 0 to 9.

131 is the smallest prime that stays prime when the end digits (on both sides) are repeated once: 11311 is also prime.

131 is the smallest integer such that the sum of its digits in every base b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 is prime.


Locomotive 131 plunges off the edge of a ravine in the movie Back to the Future Part III.

Source: Prime Curios!

509

509 is a prime number. Because 2 x 509 + 1 = 1019 is a prime, 509 is also a Sophie Germain prime.

509 is the sum of three consecutive squares: 12² + 13² + 14² = 509.

In base 4, 509 is the palindrome 13331.

509 has a representation as a sum of two squares: 509 = 5² + 22².

509 is the hypotenuse of a primitive Pythagorean triple: 509² = 220² + 459².


In the Clint Eastwood movie Firefox, 509 is the number on the conning tower of the submarine beneath the icepack.

Source: Prime Curios!

239

239 is a prime number. It is a Sophie Germain prime because 2 x 239 + 1 = 479, which is also a prime.

239 and 241 form a twin prime pair.

239 = 2 x 4³ + 4 x 3³ + 3 x 1³.

239 and 23 are the only numbers that cannot be represented in fewer than nine positive cubes (the maximum).

239 needs four squares (the maximum) to express it and 19 fourth powers (the maximum) to express it. However, 239 doesn't need the maximum number of fifth powers.

The largest prime factor of n² + 1 is at least 17, provided n is greater than 239.


The movie Pu-239, named for a radioactive isotope of the element plutonium, concerns a Russian nuclear plant worker.

Source: Wolfram MathWorld

251

251 is a prime number. It is also a Sophie Germain prime because 2 x 251 + 1 = 503 is also prime.

251 is the smallest number that is the sum of three different cubes in two ways: 251 = 1³ + 5³ + 5³ = 2³ + 3³ + 6³.

251 can be expressed using the first three primes: 251 = 2³ + 3³.

251 is a divisor of 20⁵ - 1.


Telephone area code 251 covers southwestern Alabama.

Source: Prime Curios!

641

641 is a prime number. It is a Sophie Germain prime because 2 x 641 + 1 = 1283, which is also prime.

Leonhard Euler found the first counterexample to Fermat's conjecture that 2^{2^n} + 1 is always prime, when he discovered in 1742 that 2^{2^5} + 1 is divisible by 641. All factors of 2^{2^n} + 1 are of the form k x 2^{n + 1} + 1. In this case 641 = 10 x 2⁶ + 1.

641 has a representation as a sum of two squares: 641 = 4² + 25².

641 and 643 form a twin prime pair.

641 is the hypotenuse of a primitive Pythagorean triple: 641² = 200² + 609².


The telephone area code 641 covers the central portion of Iowa.

Source: D. Wells. 1997. The Penguin Dictionary of Curious and Interesting Numbers, rev. ed.

233

233 is a prime number. It is a Sophie Germain prime because 2 x 233 + 1 = 467 is also a prime.

233 is the 13th Fibonacci number.

233 is the only known Fibonacci prime whose sum of digits is a Fibonacci number: 2 + 3 + 3 = 8.

233 has a representation as a sum of two squares: 233 = 8² + 13².

233 is the smallest number with the property that it and its neighbors can be written as a sum of two squares and therefore can be the hypotenuse of a Pythagorean triangle: 233² = 105² + 208².

2²³³ - 3 is a prime.


Had Ray Bradbury used the metric system, he may have called his novel Celsius 233 instead of Fahrenheit 451.

Source: Number Gossip